Rate of homogeneous crystal nucleation in molten NaCl

We report a numerical simulation of the rate of crystal nucleation of sodium chloride from its melt at moderate supercooling. In this regime nucleation is too slow to be studied with "brute force" molecular-dynamics simulations. The melting temperature of ("Tosi Fumi") NaCl is approximately 1060 K. We studied crystal nucleation at T = 800 and 825 K. We observe that the critical nucleus formed during the nucleation process has the crystal structure of bulk NaCl. Interestingly, the critical nucleus is clearly faceted, the nuclei have a cubical shape. We have computed the crystal-nucleation rate using two completely different approaches, one based on an estimate of the rate of diffusive crossing of the nucleation barrier, the other based on the forward flux sampling and transition interface sampling methods. We find that the two methods yield the same result within an order of magnitude. However, when we compare the extrapolated simulation data with the only available experimental results for NaCl nucleation, we observe a discrepancy of nearly five orders of magnitude. We discuss the possible causes for this discrepancy.     

Molecular mechanism of crystal nucleation from solution

Nucleation from solution is fundamental to many natural and industrial processes. The understanding of molecular mechanism of nucleation from solution is conducive to predict crystal structure, control polymorph and design desired crystal materials. In this review, the nucleation theories, including classical nucleation theory(CNT), nonclassical nucleation theory, as well as other new proposed theories, were reprised, and the molecular mechanism of these theories was compared. Then, the molecular process of nucleation, including the current study techniques, the effect of molecular self-assembly in solutions, desolvation process, as well as the properties of solvent and crystal structure on nucleation from solution were summarized. Furthermore, the relationship of molecular conformation in solution and in crystal, and the effect of solute molecular flexibility on nucleation were discussed.Finally, the current challenges and future scopes of crystal nucleation from solution were discussed.     

Molecular dynamics studies of homogeneous nucleation in solid-state transitions

Simulations of clusters containing 100 to 250 molecules of TeF₆ successfully reproduce the crystalline packing arrangements observed in electron diffraction investigations of large molecular clusters (～ 10⁴ molecules) of the same material. More remarkably, when the clusters are cooled step by step in MD computations at a rate of ca. 10¹¹ K/s they spontaneously undergo the same bcc to monoclinic phase transition that has been observed experimentally in supersonic flow, despite the million-fold difference in the timescales involved. The existence of such a correspondence over so many orders of magnitude, in itself, imposes severe constraints on what type of molecular mechanism can underlie the transformation. Even more revealing evidence about the molecular behavior associated with the phase change is provided by the simulations. They show the formation of the actual transition complexes along the transition pathway, namely, the critical nuclei of the new phase. These nuclei, which are made up of approximately 20 molecules, can be recognized in the midst of the surrounding matter. Techniques based on molecular orientations, involving Pawley-Fuchs projections and orientational angular distribution functions, make it possible to estimate the size of critical nuclei. One noteworthy result established in the simulations is that the solid-state transition temperature from bcc to monoclinic depends upon particle size in the same manner as does the freezing point.     

Molecular dynamics simulation of the crystal nucleation behavior of a single chain touching a substrate surface

Molecular dynamics simulation has been used in exploring the crystal nucleation behaviour of a single chain touching a substrate surface. It shows that a polyethylene chain (980 CH₂) changed its overall shape from an isotropic coil to an oriented one in the case of touching a substrate surface of amorphous carbons at 300 K. Most repeats of the chain were aligned and ordered in a zigzag package. Surprisingly, the direction of the package is not parallel to the plane of the substrate, but almost perpendicular to it. This is in accordance with experimental observations.     

Molecular dynamics simulation of dense carbon dioxide fluid on amorphous silica surfaces

Molecular dynamics (MD) simulations of dense carbon dioxide on the amorphous dehydroxylated silica surfaces have been carried out. The adsorption potential surfaces of the silica solids have been obtained in order to evaluate the characteristics of the amorphous surfaces. The atom density profiles, adsorption free energy profiles, surface orientation order parameters, and radial distribution functions for the CO2 molecules have been presented in order to study the effect of the amorphous surfaces on the microscopic interfacial structure properties of the CO2 molecules. The translational diffusion and orientation rotation at silica surfaces have also been investigated. It was observed that there is marked hindrance of the translational diffusion and orientation rotation of CO2 molecules near amorphous silica surfaces.     

Effect of the surface-stimulated mode on the kinetics of homogeneous crystal nucleation in droplets

The thermodynamics of surface-stimulated crystal nucleation demonstrates that if at least one of the facets of the crystal is only partially wettable by its melt, then it is thermodynamically more favorable for the nucleus to form with that facet at the droplet surface rather than within the droplet. So far, however, the kinetic aspects of this phenomenon had not been studied at all. In the present paper, a kinetic theory of homogenous crystal nucleation in unary droplets is proposed by taking into account that a crystal nucleus can form not only in the volume-based mode (with all its facets within the droplet) but also in the surface-stimulated one (with one of its facets at the droplet surface). The theory advocates that even in the surface-stimulated mode crystal nuclei initially emerge (as subcritical clusters) homogeneously in the subsurface layer, not "pseudo-heterogeneously" at the surface. A homogeneously emerged subcritical crystal can become a surface-stimulated nucleus due to density and structure fluctuations. This effect contributes to the total rate of crystal nucleation (as the volume-based mode does). An explicit expression for the total per-particle rate of crystal nucleation is derived. Numerical evaluations for water droplets suggest that the surface-stimulated mode can significantly enhance the per-particle rate of crystal nucleation in droplets as large as 10 microm in radius. Possible experimental verification of the proposed theory is discussed.     

Molecular dynamics studies to understand the mechanism of heat accommodation in homogeneous condensing flow of carbon dioxide

Using molecular dynamics (MD), we have studied the mechanism of heat accommodation between carbon dioxide clusters and monomers for temperatures and cluster size conditions that exist in homogeneous condensing supersonic expansion plumes. The work was motivated by our meso-scale direct simulation Monte Carlo and Bhatnagar-Gross-Krook based condensation simulations where we found that the heat accommodation model plays a key role in the near-field of the nozzle expansion particularly as the degree of condensation increases [R. Kumar, Z. Li, and D. Levin, Phys. Fluids 23, 052001 (2011)]. The heat released by nucleation and condensation and the heat removed by cluster evaporation can be transferred or removed from either the kinetic or translational modes of the carbon dioxide monomers. The molecular dynamics results show that the time required for gas-cluster interactions to establish an equilibrium from an initial state of non-equilibrium is less than the time step used in meso-scale analyses [R. Kumar, Z. Li, and D. Levin, Phys. Fluids 23, 052001 (2011)]. Therefore, the good agreement obtained between the measured cluster and gas number density and gas temperature profiles with the meso-scale modeling using the second energy exchange mechanism is not fortuitous but is physically based. Our MD simulations also showed that a dynamic equilibrium is established by the gas-cluster interactions in which condensation and evaporation processes take place constantly to and from a cluster.     

Atomistic simulation of the homogeneous nucleation and of the growth of N2 crystallites

We report on a computer simulation study of the early stages of the crystallization of molecular nitrogen. First, we study how homogeneous nucleation takes place in supercooled liquid N(2) for a moderate degree of supercooling. Using the umbrella sampling technique, we determine the free energy barrier of formation for a critical nucleus of N(2). We show that, in accord with Ostwald's rule of stages, the structure of the critical nucleus is predominantly that of a metastable polymorph (alpha-N(2) for the state point investigated). We then monitor the evolution of several critical nuclei through a series of unbiased molecular dynamics trajectories. The growth of N(2) crystallites is accompanied by a structural evolution toward the stable polymorph beta-N(2). The microscopic mechanism underlying this evolution qualitatively differs from that reported previously. We do not observe any dissolution or reorganization of the alpha-like core of the nucleus. On the contrary, we show that alpha-like and beta-like blocks coexist in postcritical nuclei. We relate the structural evolution to a greater adsorption rate of beta-like molecules on the surface and show that this transition actually starts well within the precritical regime. We also carefully investigate the effect of the system size on the height of the free energy barrier of nucleation and on the structure and size of the critical nucleus.     

Extended study of molecular dynamics simulation of homogeneous vapor-liquid nucleation of water

Using the simple point charge/extended water model, we performed molecular dynamics simulations of homogeneous vapor-liquid nucleation at various values of temperature T and supersaturation S, from which the nucleation rate J, critical nucleus size n(*), and the cluster formation free energy DeltaG were derived. As well as providing lots of simulation data, the results were compared with theories on homogeneous nucleation, including the classical, semi-phenomenological, and scaled models, but none of these gave a satisfactory explanation for our results. It was found that two main factors made the theories fail: (1) The average cluster structure including the nonspherical shape and the core structure that is not like the bulk liquid and (2) the forward rate which is larger than assumed by the theories by about one order of magnitude. The quantitative evaluation of these factors is left for future investigations.     

The kinetics of homogeneous and two-step nucleation during protein crystal growth from solution

Many experimental reports for the kinetics of crystal nucleation and growth, from an isothermal solution, point to a sigmoidal-like behavior for the process. Here we consider three different nucleation models from the literature and show that all lead to sigmoidal or sigmoidal-like behavior for the kinetics of nucleation. A two-step nucleation process is known to occur within certain supersaturated protein solutions, and it is demonstrated in this report how the sigmoidal law yields kinetic information for the two-step and homogeneous nucleation modes. We propose here that two-step solute-rich associates form in the solution around seed nuclei that are already present at or near the point in time when the solution is prepared. Using this hypothesis, we are able to model the time-dependent volume of the two-step phase per unit volume of solution and show that this compares well with reported experimental data. A kinetic model is given for the proposed process, which leads to a sigmoidal rate law. Additionally, a relation between the initial and final nuclei densities and the induction time is derived. As a result of this study, the conclusion is that two-step activity increases with increasing initial supersaturation or increasing salt concentration.     

Molecular dynamics study of homogeneous nucleation in supercooled clusters of sodium bromide

Molecular dynamics simulations are carried out on clusters comprised of 108, 256, 500, and 864 Na⁺Br⁻ ion pairs represented by a Born–Mayer–Hugins interaction potential. Clusters with free boundaries are chosen in order to avoid the interference with nucleation caused by periodic boundary conditions. The melting point increases with increasing size of cluster as expected. The nucleation has been found to start near the surface of a NaBr cluster. The rates of nucleation in melted clusters are estimated based on classical nucleation theory. The interfacial free energies of 73.3–76.4 mJ/m² in temperature range of 400–550 K derived from kinetics of freezing are in the same order of magnitude as those predicted by Turnbull's relation and Buckle and Ubbelohde's observation. Sizes of critical nuclei are inferred from classical expressions and Voronoi polyhedra analyses.     

From carbon dioxide to methane: homogeneous reduction of carbon dioxide with hydrosilanes catalyzed by zirconium-borane complexes

A mixture of a zirconium benzyl phenoxide complex and tris(pentafluorophenyl)borane is reported that catalyzes the hydrosilation reaction of carbon dioxide to generate methane via a bis(silyl)acetal intermediate.     

Molecular simulation of carbon dioxide/methane/hydrogen mixture adsorption in metal-organic frameworks

This work performs a systematic computational study toward a molecular understanding of the separation characteristics of metal-organic frameworks (MOFs), for which the purification of synthetic gas by two representative MOFs, MOF-5 and Cu-BTC, is adopted as an example. The simulations show that both geometry and pore size affect largely the separation efficiency, complex selectivity behaviors with different steps can occur in MOFs, and the electrostatic interactions that exist can enhance greatly the separation efficiency of gas mixtures composed of components with different chemistries. Furthermore, the macroscopic separation behaviors of the MOF materials are elucidated at a molecular level to give insight into the underlying mechanisms. The findings as well as the molecular-level elucidations provide useful microscopic information toward a complete understanding of the separation characteristics of MOFs that may lead to general design strategies for synthesizing new MOFs with tailored properties, as well as guiding their practical applications.     

Molecular dynamics simulation of the homogeneous crystallization of liquid rubidium

The homogeneous crystallization of liquid rubidium models containing 500, 998, and 1968 particles in the basic cube was studied by the molecular dynamics method. The liquid crystallized over the temperature range 70–182.5 K predominantly with the formation of a body centered cubic (BCC) structure. The mechanism of crystallization was different from that accepted in classic nucleation theory. Crystallization developed as an increase in the number of atoms with Voronoi polyhedra of the 0-6-0-8 and 0-4-4-6 types, the formation of bound groups (clusters) from these atoms, and growth of these groups as in the coagulation of an impurity from a supersaturated solution. At the initial stage, bound groups had a very loose structure and included a fairly large number of atoms with polyhedra of other types. The linear dimension of the largest group rapidly approached the basic cube size. The atoms with the 0-6-0-8 and 0-4-4-6 Voronoi polyhedra played a leading role in crystallization and activated the transition of bound group atoms with other coordination types into a BCC coordination. The probability of formation of a bound group of a given size was found to be independent of the volume of the liquid model. Cluster size fluctuations especially strong over the temperature range 180–185 K played an important role in the formation of 0608 clusters of a threshold (“critical”) size.     

Permeation of carbon dioxide through homogeneous and asymmetric polysulfone membranes

To confirm the validity of the working assumption that a thin dense skin layer in an asymmetric membrane can be essentially replaced by a thick homogeneous dense membrane, both homogeneous and asymmetric polysulfone membranes were prepared by solvent casting, and the permeation behavior of carbon dioxide through these two types of membranes was investigated. The pressure dependence of the mean permeability coefficient through an asymmetric polysulfone membrane is apparently very similar to that through a homogeneous dense membrane, following the dual mode mobility model driven by gradients of chemical potential. The dense skin layer in the asymmetric membrane can be simulated approximately by a homogeneous dense membrane from the point of view of gas sorption and diffusion.     

Molecular dynamics simulation of liquid sulfur dioxide

A previously proposed model for molecular dynamics (MD) simulation of liquid sulfur dioxide, SO(2), has been reviewed. Thermodynamic, structural, and dynamical properties were calculated for a large range of thermodynamic states. Predicted (P,V,T) of simulated system agrees with an elaborated equation of state recently proposed for liquid SO(2). Calculated heat capacity, expansion coefficient, and isothermal compressibility are also in good agreement with experimental data. Calculated equilibrium structure agrees with X-ray and neutron scattering measurements on liquid SO(2). The model also predicts the same (SO(2))(2) dimer structure as previously determined by ab initio calculations. Detailed analysis of equilibrium structure of liquid SO(2) is provided, indicating that, despite the rather large dipole moment of the SO(2) molecule, the structure is mainly determined by the Lennard-Jones interactions. Both single-particle and collective dynamics are investigated. Temperature dependency of dynamical properties is given. The MD results are compared with previous findings obtained from the analysis of inelastic neutron scattering spectra of liquid SO(2), including wave-vector dependent structural relaxation, tau(k), and viscosity, eta(k).     

High-pressure combinatorial screening of homogeneous catalysts: hydrogenation of carbon dioxide

A simple method for high-pressure combinatorial catalyst discovery with visual (dye-based) assay is described. With this method, the first highly active catalyst, incorporating metals outside the platinum group, has been identified for CO(2) hydrogenation.     

Molecular approaches to the electrochemical reduction of carbon dioxide

This article reviews recent progress in the exploitation of carbon dioxide as a chemical feedstock. In particular, the design and development of molecular complexes that can act as catalysts for the electrochemical reduction of CO(2) is highlighted, and compared to other biological, metal- and non-metal-based systems.